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scrnGC2: Calc Input
scrnGC3: f(x) Plot Input
scrnGC4: g(x) Plot Input
The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.
Incenter Help
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The incenter of a triangle is the point where the three angle bisectors of a triangle meet.
The coordinates of the incenter are a weighted average of the coordinates of the three vertices. Finding the weighted average is not a simple matter.
Incenter (x, y) = (   (a•xa + b•xb +c•xc)   /   p   ,     (a•ya + b•yb +c•yc)  /   p   )
Where:    xa , xb and xc are the x-coordinates of vertices A, B and C.
ya , yb and yc are the y-coordinates of vertices A, B and C.
a, b and c are the lengths of the sides opposite vertices A, B and C, respectively.
p is the perimeter of the triangle, p = a + b + c.
In order to find a, b and c, you must use the distance formula.
a =
  ( xb - xc ) ² + ( yb - yc ) ²
b =
  ( xa - xc ) ² + ( ya - yc ) ²
c =
  ( xa - xb ) ² + ( ya - yab ) ²
The incenter is equidistant from each of the triangle sides which means that a circle can be inscribed within the triangle as shown below.
The radius of the inscribed circle is:
r =
 ( s - a )•( s - b)•( s - c ) / s
Where:    s = p / 2
Example:  Given: A ( -7, -6 ), B ( -3, 6 ) and C ( 8, -1 )
a = 
 11² + 7²
  =  
 170
=  13.04
b = 
 15² + 5²
  =  
 250
=  15.81
c = 
 4² + 12²
  =  
 160
=  12.65
p = a + b + c = 41.50
s = p / 2 = 20.75
incenter(x,y) = ((-7a-3b+8c)/p , (-6a+6b-1c)/p) = (-0.9, 0.1)
r =
 ( s - a )•( s - b)•( s - c ) / s
=  3.86

© 2002- John Schlecht. All rights reserved.